Quantifying necessary quantum resources for nonlocality

Nonlocality is one of the most important resources for quantum information protocols. The observation nonlocal correlations in a Bell experiment result appropriately chosen measurements and states. We quantify minimal purity to achieve certain value any operator. Since fundamental resource state, this enables us also necessary coherence, discord, entanglement given violation two-qubit correlation inequalities. Our results shine new light on CHSH inequality by showing that fixed an increase measurement does not always lead decrease state resources.